Economics at your fingertips  

Time-consistent mean–variance portfolio optimization: A numerical impulse control approach

Pieter M. Van Staden, Duy-Minh Dang and Peter A. Forsyth

Insurance: Mathematics and Economics, 2018, vol. 83, issue C, 9-28

Abstract: We investigate the time-consistent mean–variance (MV) portfolio optimization problem, popular in investment–reinsurance and investment-only applications, under a realistic context that involves the simultaneous application of different types of investment constraints and modelling assumptions, for which a closed-form solution is not known to exist. We develop an efficient numerical partial differential equation method for determining the optimal control for this problem. Central to our method is a combination of (i) an impulse control formulation of the MV investment problem, and (ii) a discretized version of the dynamic programming principle enforcing a time-consistency constraint. We impose realistic investment constraints, such as no trading if insolvent, leverage restrictions and different interest rates for borrowing/lending. Our method requires solution of linear partial integro-differential equations between intervention times, which is numerically simple and computationally effective. The proposed method can handle both continuous and discrete rebalancings. We study the substantial effect and economic implications of realistic investment constraints and modelling assumptions on the MV efficient frontier and the resulting investment strategies. This includes (i) a comprehensive comparison study of the pre-commitment and time-consistent optimal strategies, and (ii) an investigation on the significant impact of a wealth-dependent risk aversion parameter on the optimal controls.

Keywords: Asset allocation; Constrained optimal control; Time-consistent; Pre-commitment; Impulse control (search for similar items in EconPapers)
JEL-codes: G11 C61 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed

Downloads: (external link)
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Dana Niculescu ().

Page updated 2019-01-19
Handle: RePEc:eee:insuma:v:83:y:2018:i:c:p:9-28